Existence and Concentration Solutions for a class of elliptic PDEs involving p-biharmonic Operator

2016/06/08 by Giri, Ratan Kr, Choudhuri, Debajyoti, Pradhan, Shesadev
#35J35 #35J60 #35J92 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1606.02512

Abstract

In this paper, we propose an existence result pertaining to a nontrivial solution to the problem \\beginsplit amp; Δ²_p u -Δ_p u + λV(x)|u|^p-2u = f(x,u) , x∈ ℝ^N, amp; u ∈ W^2,p(ℝ^N), \endsplit where λ>0, p>1, N>2p and V∈ C(ℝ^N, ℝ⁺), f∈ C(ℝ^N × ℝ,ℝ) with certain properties. We also investigate the concentration of solutions to the problem on the set V^-1(0) as λ→ ∞.

Related

• Semilinear elliptic PDE's with biharmonic operator and a singular potential
• Existence of multi-bump solutions for a class of elliptic problems\n involving the biharmonic operator
• On a biharmonic equations with steep potential well and indefinite potential
• Biharmonic equation with singular nonlinearity
• Some remarks on biharmonic elliptic problems with a singular nonlinearity